source string | id string | question string | options list | answer string | reasoning string |
|---|---|---|---|---|---|
AQUA-RAT | AQUA-RAT-38197 | Difficulty:
65% (hard)
Question Stats:
53% (03:18) correct 47% (03:14) wrong based on 97 sessions
### HideShow timer Statistics
Question of the Week #7
Three pipes P, Q, and R are attached to a tank. P and Q individually can fill the tank in 3 hours and 4 hours respectively, while R can empty the tank in 5 hours.... | [
"6",
"7",
"8",
"9"
] | A | The part filled by A + B + C in 1 hour is 1/10 + 1/20 + 1/60 = 1/6
All the three pipes together will fill the tank in 6 hours.
The answer is A. |
AQUA-RAT | AQUA-RAT-38198 | human-biology, reproduction, anthropology
Note: here is a link about multiple pregnancy : https://www.healthline.com/health/pregnancy/chances-of-having-twins#assisted-reproduction. 49 - 19 = 30
So the 1st Child would be 30 when the last children would be born, as long as the parents stay healthy and the mother deliver... | [
"33",
"40",
"38",
"27"
] | B | Explanation:
Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.
Sum of the present ages of wife and child (20 x 2 + 5 x 2) years = 50 years.
Husband's present age = (90 - 50) years = 40 years.
Answer: B) 40 |
AQUA-RAT | AQUA-RAT-38199 | # Reset the equation counter
\documentclass{article}
\usepackage{amsmath, amsfonts, chngcntr}
\newcounter{problem}
\newcounter{solution}
\newcommand\Problem{%
\stepcounter{problem}%
\textbf{\theproblem.}~%
\setcounter{solution}{0}%
}
\newcommand\TheSolution{%
\textbf{Solution:}\\%
}
\newcommand\ASolution{%
\stepcou... | [
"6",
"7",
"8",
"9"
] | B | Explanation:
Rate downstream = (20/2) kmph = 10 kmph;
Rate upstream = (20/5) kmph = 4 kmph
Speed in still water = 1/2 (10 + 4) kmph = 7 kmph
ANSWER: B |
AQUA-RAT | AQUA-RAT-38200 | # Clarification on language of a question on profit and loss.
The question is:
By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage.
1. 33 1/3%
2. 33 1/2%
3. 33%
4. 34 1/4%
The answer provided by the book says it's the first one.
But if he gains the cost of 11 meters sh... | [
"Rs.21136.36",
"Rs.31136.36",
"Rs.51136.36",
"Rs.61136.36"
] | C | Explanation:
S.P = Rs.54,000. Gain earned = 20%
C.P = Rs.[100/120×54000]
=Rs. 45000
This is the price the first person sold to the second at at loss of 12%.
Now S.P = Rs.45000 and loss = 12%
C.P. Rs.[100/88×45000]= Rs.51136.36
Correct Option : C |
AQUA-RAT | AQUA-RAT-38201 | reference-request, modelling, voting
For the election $(C, \{v\})$, i.e. with $v$ being the only vote, we have two admissible outcomes: $O_1 = \{p_\mathrm{rep} \mapsto 1, p_\mathrm{dem} \mapsto 0\}$ and $O_2 = \{p_\mathrm{rep} \mapsto 0, p_\mathrm{dem} \mapsto 1\}$. For $(C, \{v, v\})$, we have the same two outcomes. ... | [
"2800",
"1980",
"2900",
"2200"
] | B | B
Number of valid votes = 80% of 5500 = 4400.
Valid votes polled by other candidate = 45% of 4400
= (45/100 x 4400) = 1980. |
AQUA-RAT | AQUA-RAT-38202 | \limits_{C_{1}}=\frac{5}{6}.\frac{4^6}{4^4}+\frac{1}{5}.\frac{4^5}{4^2}-12=\frac{40}{3}+\frac{64}{5}-12$ For C2 we have x=2, dx=0 $\therefore \int\limits_{C_{2}}=\int\limits_{-4}^{4}(4y+3)dy=[2y^2+3y]_{-4}^{4}=32+12-32+12=24$ for C3 we have $\int\limits \limits_{C_{3}}=\int\limits_{4}^0(\frac{5y^5}{4^4}-\frac{y^4}{4^2}... | [
"550 meters",
"3.3 meters",
"100 meters",
"3.5 meters"
] | B | Solution:
1 meter = 100 centimeters
Just divide 330 by 100
330 ÷ 100 = 3.3, so there are 3.3 meters in 330 centimeters
Option B |
AQUA-RAT | AQUA-RAT-38203 | ### Show Tags
23 Dec 2016, 09:03
2x+50/5x+40=4/6, find x, then don't get into decimals, approx 17.something then 2(17)+5(17)= approx 122
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9558
Location: Pune, India
Re: Two mixtures A and B contain milk and water in the ratios [#permalink]
### Show Tags
09 Nov ... | [
"40",
"44",
"47",
"83"
] | B | Explanation:
Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.
Answer: Option B |
AQUA-RAT | AQUA-RAT-38204 | solution: solution to get the median: the mean compared to sets a mean questions with solutions b Question! To new CBSE exam Pattern, MCQ questions for Class 10to help you are presented 6 ICSE.. A- a ; each being equal to the common difference we will help you sum must 12! Step 3: the given mean of a set of numbers dee... | [
"3",
"4",
"5",
"6"
] | D | Here Mean => 1+2+3/3 => 2
median => 2
and range => 3-1 => 2
hence sum => 2+2+2 => 6
Answer: D |
AQUA-RAT | AQUA-RAT-38205 | special-relativity, speed-of-light, reference-frames
Title: Relative speed when approaching the speed of light According to this chart of the Lorentz factor as a function of speed:
If a spacecraft neared (roughly) 0.85c, would it appear to be traveling at 1.7x the speed of light from the perspective of those on boar... | [
" 1,11 * 10^7",
" 6,70 * 10^7",
" 1,11 * 10^8",
" 1,86 * 10^8"
] | B | The easiest way to answer this question is by POE, it does not require any calculation (answered in 30seconds). In one hour there are 3600 seconds, therefore speed in miles/hour will be.
(1.86*10^4)*3600 = (1.86*10^4)*(3.6*10^3) = some number*10^7...
The key is realizing that thesome numberhas to be bigger thatn 1.86 (... |
AQUA-RAT | AQUA-RAT-38206 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$v = u – at$$ $$=> 30 = 60 – 1xt$$ $$=> t = 30s$$ At 30s, distance covered is: $$S = ut – ½ at^2$$ $$= 60 x 30 – ½ x 1 x (30)2$$ $$= 1800 – (15 x 30)$$ $$= 1800 – 450$$ $$= 1350m$$ (from the initial 90... | [
"32 sec",
"42 sec",
"45 sec",
"18 sec"
] | A | total length= 280+200=480
speed=54km/h=(54*5)/18= 15/1m/s
time=(480*1)/15=32 sec.
ANSWER:A |
AQUA-RAT | AQUA-RAT-38207 | a-5/a+2 = -1
a-5= -a-2
0= -2a+3
subtract 3 from both sides:
-3=-2a
Divide by -2
3/2=a
I know that the answer is (-2, 3/2), but I'm not sure where the -2 in the answer comes from. Thanks!
You have to be wary with inequalities because it changes direction if you multiply or divide by a negative so ideally we don't w... | [
"40",
"45",
"35",
"55"
] | B | Multiply all terms of the given equation by (a - 5)(a + 5), simplify and solve
(a - 5)(a + 5)[ 4/(a - 5) ] = (a - 5)(a + 5) [5/(a + 5) ]
4 (a + 5) = 5 (a - 5)
a =45
correct answer B |
AQUA-RAT | AQUA-RAT-38208 | Sol:
Folks, look at the relative calculation here.
If we consider that all the 120 candidates passed the examination, the average of the entire class must be 39. But it is given that average of the entire class is 35.
So we are getting an extra of 4 in the average i.e. an extra of 4x120=480 in the total sum.
We got... | [
"40",
"52",
"65",
"80"
] | C | let the no of matches played more=x
so,
(120+x)*52/100=31.2+x
by solving we get x=65
ANSWER:C |
AQUA-RAT | AQUA-RAT-38209 | in the comments section. At what speed does the second train B travel if the first train travels at 120 km/h. You can approach this as if you were solving for an unknown in math class or you can use the speed triangle. Time, Speed and Distance: Key Learnings. ) Since the distances are the same, I set the distance expre... | [
"20",
"30",
"48",
"56"
] | D | Total distance = 72
Distance = Speed * Time
Walking speed = s1 = 8
Walking time = t1
Bike speed = s2 = 16
Time traveled in bike = t2
d1 + d2 = 72
s1t1 + s2t2 = 72
8*t1 + 16*t2 = 72
t1 + 2*t2 = 9 ----- (1)
Given: t1 + t2 = 8 ----- (2)
(1) - (2) --> t2 = 1 and t1 = 8 - 1 = 7
Walking distance = s1*t1 = 8*7 = 56
Answer: D |
AQUA-RAT | AQUA-RAT-38210 | # Permutations of the word $\text{TRIANGLE}$ with no vowels together.
First of all, $$\text{TRIANGLE}$$ has $$8$$ distinct letters, $$3$$ of which are vowels($$\text{I, A, E}$$) and rest are consonants($$\text{T, R, N, G, L}$$).
While attempting this, I came up with the idea of putting alternate vowels and consonants... | [
"D",
"E",
"S",
"P"
] | B | The first, fourth, seventh and eleventh letters of the word 'SPHERVLVODS'
The word formed is LESS
The second letter is E.
ANSWER B |
AQUA-RAT | AQUA-RAT-38211 | 2-4-8-6
2-4-8-6
2-4
The next digit in the pattern will be 8, which will belong to $$2^{11}$$.
In fact, any integer that ends with 2 and is raised to the power 11 will end in 8 because the last digit will depend only on the last digit of the base.
So $$652^{11}$$ will end in $$8,1896782^{11}$$ will end in 8, and so... | [
"0",
"1",
"3",
"5"
] | B | We do not have to do any calculations or find units digit of remaining numbers...
all three terms - 11,1,21 - are ODD and since the PRODUCT contains 1, the units digit of the product will remain 1
B |
AQUA-RAT | AQUA-RAT-38212 | induction that the product of three consecutive integers is divisible by 6. Real numbers class 10. In mathematics, the least common multiple, also known as the lowest common multiple of two (or more) integers a and b, is the smallest positive integer that is divisible by both. Click 'show details' to verify your result... | [
"21",
"24",
"27",
"32"
] | D | Let the 3 consecutive odd numbers each divisible by 3 be X, X+3, X+6
Given, X + X+3 + X+6 =87
3X = 78
X = 26
The numbers are 26, 29, 32
Therefore the largest number is 32
Answer D. |
AQUA-RAT | AQUA-RAT-38213 | # Reset the equation counter
\documentclass{article}
\usepackage{amsmath, amsfonts, chngcntr}
\newcounter{problem}
\newcounter{solution}
\newcommand\Problem{%
\stepcounter{problem}%
\textbf{\theproblem.}~%
\setcounter{solution}{0}%
}
\newcommand\TheSolution{%
\textbf{Solution:}\\%
}
\newcommand\ASolution{%
\stepcou... | [
"20 km/hr",
"22 km/hr",
"28 km/hr",
"30 km/hr"
] | B | Let the speed of the boat in still water =x km/hr
Speed of the current = 2 km/hr
Then, speed downstream =(x+2) km/hr
speed upstream =(x−2) km/hr
Total time taken to travel 10 km upstream and back = 55 minutes =5560 hour = 1112 hour
⇒10x−2+10x+2=1112 120(x+2)+120(x−2)=11(x2−4) 240x=11x2−44 11x2−240x−44=0 11x2−242x+2x−44... |
AQUA-RAT | AQUA-RAT-38214 | Probability of more than 1 goal at the end of a match
Probability of a match ending with
- 0 goals is 40%,
- 1 goal is 45% and
- more than 1 goal is 15%.
Now at half-time, the score is 1-0.
What is the probability of more than 1 goal at the end of the match?
A. Is it still 15%, or
B. is it 25% (100% = probability of... | [
"0",
"1",
"2",
"3"
] | B | Total number of students = 8+2+5= 15
so median must be the middle term out of the 15 terms i.e., 8th term when arranged in ascending order
arranging in ascending order we have {1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3}
median number of goals scored per student = 1
ANSWER:B |
AQUA-RAT | AQUA-RAT-38215 | Puzzle of gold coins in the bag
At the end of Probability class, our professor gave us the following puzzle:
There are 100 bags each with 100 coins, but only one of these bags has gold coins in it. The gold coin has weight of 1.01 grams and the other coins has weight of 1 gram. We are given a digital scale, but we ca... | [
"220",
"240",
"260",
"280"
] | D | Value is given in the ratio 8:4:2.
(8x/0.25) + (4x/0.5) + (2x/1) = 840.
X = 20. Total amount = 14*20 = 280
Answer:D |
AQUA-RAT | AQUA-RAT-38216 | Case 1: (3,1,1) First choose which of the 3 pockets will get three marbles. There are 3C1 =3 ways to do this. Then, choose the number of ways we can place 3 marbles into that box from 5 marbles. There are 5C3 = 10 ways to do this. Next we must place a marble in the next to the last box. There are 2C1 = 2 ways to do thi... | [
"7",
"8",
"9",
"10"
] | D | The worst case scenario would be that he has taken 4 blue and 5 green, a total of 9 marbles, and still doesn't have 3 distinct colors. But the next draw will surely be red as only the red marbles are left in his pocket.
The answer is D. |
AQUA-RAT | AQUA-RAT-38217 | # Simple and Compound Interest Problem
• January 14th 2011, 01:41 AM
dumluck
Simple and Compound Interest Problem
Hi All,
Q:Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest be... | [
"Rs.3100",
"Rs.2700",
"Rs.2200",
"Rs.1800"
] | B | Explanation :
Let the man invests Rs.x at 6% and Rs.y at 7%
Simple Interest on Rs.x at 6% for 2 years + Simple Interest on Rs.y at 7% for 2 years = Rs.354
x × 6 ×2 /100+y×7×2/100=354
x × 6 × 2+y×7×2=354×100
x × 6+y × 7=177×100
6x+7y=17700⋯(1)
One-forth of the first sum is equal to one-fifth of the second sum
=>x/4=y/5
... |
AQUA-RAT | AQUA-RAT-38218 | When I tested my answer and the book's, I found out that the book's answer gave the fraction that I was asked to break up.
Is there a reason why I must factorise the denominator into (1-x)^2 (1+x) and not (x-1)^2 (1+x)?
hi
you are correct and the book is also correct. You just play with the algebra here.
-1/4(x-1)=... | [
"-1",
"2",
"1",
"-2"
] | D | If we solve the question, we get x=-2.
Option: D |
AQUA-RAT | AQUA-RAT-38219 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$v = u – at$$ $$=> 30 = 60 – 1xt$$ $$=> t = 30s$$ At 30s, distance covered is: $$S = ut – ½ at^2$$ $$= 60 x 30 – ½ x 1 x (30)2$$ $$= 1800 – (15 x 30)$$ $$= 1800 – 450$$ $$= 1350m$$ (from the initial 90... | [
"a) 45",
"b) 33",
"c) 48",
"d) 55"
] | C | Let y be the balance distance to be covered and x be the former speed.
A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late
so, y/(3x/4) - y/x = 35/60
4y/3x - y/x = 7/12
y/x(4/3-1)=7/12
y/x*1/3=7/12
y/x=7/4
4y-7x=0 ........ 1... |
AQUA-RAT | AQUA-RAT-38220 | Thus,
200 x 0.3 = 60 received student loans
200 x 0.4 = 80 received scholarships
We are trying to determine what percent of those surveyed said that they had received neither student loans nor scholarships.
Let’s fill all this information into a table. Note that each row sums to create a row total, and each column ... | [
"56%",
"64%",
"80%",
"82%"
] | C | Those who support = 40.
% of those who don't support it is (200-40)/ 200 = 80%
Answer C |
AQUA-RAT | AQUA-RAT-38221 | 1 = 1
4 = 2^2
6 = 2 * 3
9 = 3^2
13 = 13
16 = 2^4
22 = 2 * 11
24 = 2^3 * 3
25 = 5^2
33 = 3 * 11
36 = 2^2 * 3^2
37 = 37
46 = 2 * 23
49 = 7^2
52 = 2^2 * 13
54 = 2 * 3^3
61 = 61
64 = 2^6
69 = 3 * 23
73 = 73
78 = 2 * 3 * 13
81 = 3^4
88 = 2^3 * 11
94 = 2 * 47
96 = 2^5 * 3
97 = 97
100 = 2^2 * 5^2
109 = 109
117 = 3^2 * 13
118... | [
"2337",
"1227",
"3327",
"5457"
] | A | According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
2344 - 12*3*2 = 2344 - 8 = 2337
correct answer A |
AQUA-RAT | AQUA-RAT-38222 | A boy and his sister. When you subtract two from the boy’s real age and add two to his sister’s age, his sister
becomes twice his NEW (subtracted) age. If you subtract three from his real age instead and add three to his sister then she becomes thrice his NEW (subtracted) age. What are their real ages?
A little more de... | [
"25",
"30",
"45",
"60"
] | B | Explanation:
Let their ages 10 years ago is x, 2x and 3x years.
10 + 2x + 10 + 3x + 10 = 90 hence x= 10
B’s present age = (2x + 10) =30 years
Option B |
AQUA-RAT | AQUA-RAT-38223 | # Calculate the number of ways to paint $5$ buildings with $4$ colours such that all $4$ colours must be used
A developer has recently completed a condominium project in a valley. There are blocks of buildings $A$, $B$, $C$, $D$ and $E$ as shown in the diagram below.
The developer has colours available to paint the b... | [
" 0.8(80 – y)",
" 0.8 + 0.0025y",
" 80/y – 1.25",
" 80/1.25y"
] | B | This may be a case of bad numberpicking but it worked for me.
80 houses. Let's say that y=40 houses are painted at the rate x=10 houses per week <=> 1/10 week per house. 40*1/10 = 4 houses per week will be painted at this rate.
80-y = 80-40 = 40 houses are to be painted at the faster rate. X*1,25=12,5 houses per week <... |
AQUA-RAT | AQUA-RAT-38224 | • so $x=12$ or $x=-14$
Let $$\mathbb S$$ be a set of all even integers, i.e:
$$\mathbb S = \{x | x = 2k, k\in \mathbb Z \}$$
Suppose we have two consecutive elements $$x_1$$ and $$x_2$$ in the set $$\mathbb S$$, i.e:
$$x_1 = 2k$$ ...(1)
$$x_2=2k+2$$ ...(2)
...such that their product is 168, i.e:
$$(2k)(2k+2)=168... | [
"I only",
"II only",
"I and II only",
"II and III only"
] | D | Since -4 is in the set, then the set must also include -2, 0, 2, 4, etc...
Depending on whether -4 is the starting element in the set or not, we can have -6...or not.
The answer is D. |
AQUA-RAT | AQUA-RAT-38225 | F1 = { 0/1, 1/1 }
F2 = { 0/1, 1/2, 1/1 }
F3 = { 0/1, 1/3, 1/2, 2/3, 1/1 }
F4 = { 0/1, 1/4, 1/3, 1/2, 2/3, 3/4, 1/1 }
F5 = { 0/1, 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 1/1 }
F6 = { 0/1, 1/6, 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 1/1 }
F7 = { 0/1, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 2/5, 3/7, 1/2, 4/7, 3/5, ... | [
"7/45",
"2/45",
"4/15",
"1/30"
] | D | Explanation:
HCF of Fractions = HCF of Numerators/LCM of Denominators
= (HCF of 2, 4, 6)/(LCM of 3, 12, 5) = 2/60 = 1/30
Answer: Option D |
AQUA-RAT | AQUA-RAT-38226 | # If we select a random integer number of the set $[1000000]$ what is the probability of the number selected contains the digit $5$?
If we select a random integer number of the set $[1000000]$ what is the probability of the number selected contains the digit $5$?
My work:
We know the sample space $S:$"The set of num... | [
"1/5",
"2/5",
"1",
"3/5"
] | C | We know that the sum of two numbers picked was 3. So, there could be the following cases:
(1, 2);
(2, 1);
Total of 2 cases out of which 2 have 1, thus the probability is 2/2=1.
Ans C |
AQUA-RAT | AQUA-RAT-38227 | {BB, BG, GB, GG}
From these possible combinations, we can eliminate the GG combination since we know that one child is a boy. The three remaining possible combinations are:
{BB, BG, GB}
In these combinations there are four boys, of whom we have chosen one. Let's identify them from left to right as B1, B2, B3 and B4.... | [
"4",
"5",
"2",
"3"
] | D | Explanation :
As per the question, we need to satisfy three
conditions namely:
1. Adults (A) > Boys (B)
2. Boys (B) > Girls (G)
3. Girls (G) > Families (F)
Clearly, if the number of families is 2, maximum number of adults can only be 4. Now, for the second condition to be satisfied, every family should have atleast two... |
AQUA-RAT | AQUA-RAT-38228 | 1. Let total distance=X.
1st distance =30x/100.Speed=20kmph
2nd distance=60x/100 Speed=40kmph
3rd distance=10x/100Speed=10kmph
T1=1/20*30x/100 = 3x/200
T2=1/40*60x/100 =3x/200
T3=1/10*10x/100 =X/100
Applying S=D/T Formula
30x/100+60x/100+10x/100
______________________________
3x/200+ 3x/200+ X/100.
=100x*200/8x*100
=25... | [
"75 m.",
"80 m.",
"150 m.",
"100 m."
] | D | ratio of speeds of a and b is 2:1
b is 50m away from a but we know that a covers 1 meter(2-1) more in every second than b
the time taken for a to cover 50m is 50/1=50m
so the total time taken by a and b to reach =2*50=100m
ANSWER:D |
AQUA-RAT | AQUA-RAT-38229 | In other words, the measured rectified average voltage will be multiplied by about 1.11 to get the indicated value.
To answer the first part of the question, you need to find $V_{avg}$ for the sawtooth waveform, which you have already correctly done and found it to be 5V.
What the meter will then do is multiply that ... | [
"1300",
"1400",
"2400",
"2500"
] | D | It means that 0.08% of x = 2
(8100×100 ×x)=2
x=2×100×1008
x=2500
ANSWER :D |
AQUA-RAT | AQUA-RAT-38230 | a) How long does it take to stop (time)?
b) How far does it travel before it stops?
Can you work that out?
9. Oct 25, 2016
Yes.
a)
v1=v0+a0(t1-t0)
t1=1.93 s
b)
v12=v02+2a0(x1-x0)
-182.25=-14x1
x1=13.02 m
10. Oct 26, 2016
### PeroK
So, you need to start decelerating $13.02m$ before the point you want to stop. And... | [
"a) 10",
"b) 11",
"c) 12",
"d) 20"
] | D | 0.8 minutes --> 1 mile
1 minute --> 1/0.8 = 10/8 = 1.25 miles/minute
Distance covered in 40 minutes = 1.25 * 40 = 12.5 * 4 = 50 miles
Distance covered in the current direction = Distance covered from the opposite direction (since car returns back to starting point)
Let x be the miles driven before turning
10 + x = 50 -... |
AQUA-RAT | AQUA-RAT-38231 | # Analyzing a mixture issue.
I am having a problem with this question:
Coffee A costs $75$ cents per pound and coffee B costs $80$ cents per pound to form a mixture that costs $78$ cents per pound.IF there are $10$ pounds of Mixture how many pounds of Coffee A are used?
According to the text the answer is 4. I don't... | [
"50",
"60",
"80",
"100"
] | B | Let the price of tea and coffee be x per kg in June.
Price of tea in July = 1.2x
Price of coffee in July = 0.8x .
In July the price of 1/2 kg (600gm) of tea and 1/2 kg (600gm) of coffee (equal quantities) = 60
1.2x(1/2) + 0.8x(1/2) = 60
=> x =60
Thus proved...option B. |
AQUA-RAT | AQUA-RAT-38232 | # Clarification on language of a question on profit and loss.
The question is:
By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage.
1. 33 1/3%
2. 33 1/2%
3. 33%
4. 34 1/4%
The answer provided by the book says it's the first one.
But if he gains the cost of 11 meters sh... | [
"392",
"424",
"375",
"273"
] | C | C
375
CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
75 ----- ? => 375 |
AQUA-RAT | AQUA-RAT-38233 | electric-circuits, electric-current, electrical-resistance
Title: Resistors in parallel - finding total current
I am given this circuit, where $R_1 = 4.00 \Omega$, $R_2=8.00 \Omega$, and $R_3 =5.00\Omega$. I was given by the problem statement that $I_2$, the current through $R_2$ is $I_2=4\text{A}$. I found the curre... | [
"2(R1+R2):(R1+2R2)",
"(R1+R2):(R1+2R2)",
"(2R1+R2):(R1+2R2)",
"2(R1+R2):(2R1+R2)"
] | A | two resistors A (r1) and B (r2).
total or sum of two resistors appear as
r1r2/r1+r2. It is looks like inversion of sum of rates.
1/r1+1/r2= r1+r2/r1r2.
same way sum of A(r1) and c(2r2)=1/r1+1/2r2
=2r2+r1/r12r2.
inversion rate = r12r2/2r2+r1.
ratio W of sum of a and c/sum of a and b=2r2r1/2r2+r1*r1+r2/r1r2
=2(r1+r2)/2r2... |
AQUA-RAT | AQUA-RAT-38234 | So the 1st question you needed to answer was how much distance do they cover together per hour (we just did that), now the next question to answer is how long it takes to cover 810km in total distance at their effective speed.
• it means that if they are covering 135km each our then they would be meet together in 135x... | [
"1 hour",
"1 hour 20 minutes",
"2 hours 30 minutes",
"1 hour 40 minutes"
] | B | v1 and V2 are speeds.
v1.t /50 = v2
v2.t/40 = v1
v1/v2 = 5/4
which train A would 50. 4/5 mins to cover the same distance
40 + 40 = 80 mins (ANS B) |
AQUA-RAT | AQUA-RAT-38235 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$v = u – at$$ $$=> 30 = 60 – 1xt$$ $$=> t = 30s$$ At 30s, distance covered is: $$S = ut – ½ at^2$$ $$= 60 x 30 – ½ x 1 x (30)2$$ $$= 1800 – (15 x 30)$$ $$= 1800 – 450$$ $$= 1350m$$ (from the initial 90... | [
"5 mins",
"3 mins",
"7 mins",
"9 mins"
] | B | D = 25 * 60 + 1500 = 3000 m
T = 3000/60 * 18/5 = 180 sec = 3 mins
Answer: B |
AQUA-RAT | AQUA-RAT-38236 | meters (m), centimeters (cm) & millimeters (mm). This packet covers all you need to know about sectors of a circle. The curved part of the sector is of the circumference of the circle but to find the perimeter of the sector we must add (the radius of the circle is) so the perimeter of the sector is. A worksheet where y... | [
"4457",
"4567",
"5943",
"4547"
] | C | Explanation:
Area = (17.56 x 10000) m2= 175600 m2.
ΠR2 = 175600 ⇔ (R)2 = (175600 x (7/22)) ⇔ R = 236.37 m.
Circumference = 2ΠR = (2 x (22/7) x 236.37) m =1485.78 m.
Cost of fencing = Rs. (1485.78 x 4) = Rs. 5943.
Answer: Option C |
AQUA-RAT | AQUA-RAT-38237 | Since we are not interested on the numerical value of this equation, but that the result of the equation to be an integer, not a fraction, the n outside of the parenthesis is irrelevant.
So the equation could be written as, (3n ± 1)/2, and the result of this equation is always an integer for any odd or even value of n... | [
"Both 6 and 12",
"6 only",
"12 only",
"None of these"
] | A | Explanation :
6n2 + 6n = 6n(n + 1)
Hence 6n2 + 6n is always divisible by 6 and 12 (∵ remember that n(n + 1) is always even) Answer : Option A |
AQUA-RAT | AQUA-RAT-38238 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$v = u – at$$ $$=> 30 = 60 – 1xt$$ $$=> t = 30s$$ At 30s, distance covered is: $$S = ut – ½ at^2$$ $$= 60 x 30 – ½ x 1 x (30)2$$ $$= 1800 – (15 x 30)$$ $$= 1800 – 450$$ $$= 1350m$$ (from the initial 90... | [
"5 sec",
"10 sec",
"12 sec",
"18 sec"
] | B | Answer : B.
Speed of the train relative to man = (62 - 8) kmph
= (54* 5/18) m/sec = 15m/sec
Time taken by the train to cross the man
= Time taken by It to cover 150 m at 15 m / sec = 150 *1/ 15 sec = 10sec |
AQUA-RAT | AQUA-RAT-38239 | javascript, datetime, converting
if(minutes < 10) minutes = '0' + minutes;
return hours + ':' + minutes + ' ' + suffix;
}
totalMinutes rolls over after rounding, so passing in 23.999 is equivalent to passing in 0, and 27 becomes 3, etc.
hours also roll over but start at 12 instead of zero, then 1, 2, 3 and so on... | [
" (490-x)/60",
" (480-x)/60",
" (470-x)/60",
" 60 (60 – x + 7)"
] | A | Let's just say that X is equal to 10 so we will have that the number of hours will be 8, this is our target value. Now plug 10 in the answer choices to see which gives 8.
A is correct here. |
AQUA-RAT | AQUA-RAT-38240 | It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: $$\frac{3}{w}+\frac{2}{m}=\frac{1}{6}$$.
3 men would do the same work 5 days sooner than 9 women --> $$\frac{m}{3}+5=\frac{w}{9}$$.
Solving: $$m=15$$ and $$w=90$$. $$\frac{w}{m}=6$$.
bunuel, pls help
if i equate time i am n... | [
"16",
"88",
"29",
"14"
] | A | P = 3Q
P + Q = 3Q + Q = 4Q
These 4Q people can do the work in 12 days, which means Q can do the work in 48 days.
Hence, P can do the work in 16 days. Answer: A |
AQUA-RAT | AQUA-RAT-38241 | So the 1st question you needed to answer was how much distance do they cover together per hour (we just did that), now the next question to answer is how long it takes to cover 810km in total distance at their effective speed.
• it means that if they are covering 135km each our then they would be meet together in 135x... | [
" 100",
" 120",
" 140",
" 150"
] | B | Case 1:
let rate = R, Time = T, and Distance =D
so D=RT
Case 2:
(D+60)=(R+5)(T+1)
Case 3:
(D+X)=(R+10)(T+2)
X=120
Ans B |
AQUA-RAT | AQUA-RAT-38242 | We're asked for the price at which the TOTAL PROFIT from the sale of these units = $42,000. Since there are 600 units, then each unit has to bring in$42,000/600 = $70 in profit. The COST of each unit is$90, so to hit that total profit, we just need to increase that $90 by$70 on each unit.
$90 +$70 = $160 Final Answer:... | [
"110",
"330",
"220",
"440"
] | B | 300(x-30)≥30,000
x-30≥300
x≥330
Answer: Option B |
AQUA-RAT | AQUA-RAT-38243 | ### Show Tags
07 Nov 2012, 05:44
breakit wrote:
Bunuel wrote:
breakit wrote:
Hi I couldn't able to understand the write uo which i have marked in red . Please help here..(not sure how to mark those picture stuff)
Check here: if-2-different-representatives-are-to-be-selected-at-random-128233.html#p1113622
Hope it he... | [
"25",
"40",
"50",
"60"
] | B | 120 = 60(Mac) + x(Window) + 20(both) => x=40
ANSWER:B |
AQUA-RAT | AQUA-RAT-38244 | electromagnetism
Title: What happens if I crush a neodymium magnet into powder? There are a couple questions here. Will it retain its magnetism? Can I add the powder to the iron powder currently in my "magnetic" silly putty to make it truly magnetic? And finally, how best do I crush it? The magnet that came with the p... | [
"100bd/m",
"100m/(bd)",
"bd/(100m)",
"m/(bd)"
] | D | crate has = bd magnates
C crate cost = m dollars = 100 m cents
each magnate cost for each crate = m / bd
Ans; D |
AQUA-RAT | AQUA-RAT-38245 | Aren't there 2 possible answers for #1?
x=5, y=2
x=25, y=1
Thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 52344
### Show Tags
31 Mar 2014, 00:26
1
karimtajdin wrote:
walker wrote:
jimjohn wrote:
1. z is prime and is 3. So, x=5 SUFF.
Aren't there 2 possible answers for #1?
x=5, y=2
x=25, y=1
Thanks!
Notice that we... | [
"11",
"15",
"12",
"17"
] | C | C
12
(X + Y) – (Y + Z) = 12
X – Z = 12 |
AQUA-RAT | AQUA-RAT-38246 | 4. As great is this is, i have found an arithmetic error in the solution that has left me hanging once again!
$(2V/pi)=4r^3$ He divided each side by 2 to get...
$2r^3=(4V/pi)$ But wouldn't dividing by 2 give you $2r^3=(V/pi)$ ?
You would then get $r=\sqrt[3](V/2pi)$ thus $d=2r=2\sqrt[3](V/pi)$.
What would you do no... | [
"64",
"8",
"1/4",
"1/8"
] | C | Say r=2 => V1 = 16
when r=1; V2 = 4
V2 = 1/4*V1.
Answer : C |
AQUA-RAT | AQUA-RAT-38247 | Hint: Find the square of $1+\sqrt{3}$. ${}{}{}{}{}{}{}{}{}$
-
Since $(4+2\sqrt3)(4-2\sqrt3)=16-12=4$, try squaring: \begin{align} \left(\sqrt{4+2\sqrt3}+\sqrt{4-2\sqrt3}\right)^2 &=(4+2\sqrt3)+(4-2\sqrt3)+2\sqrt{(4+2\sqrt3)(4-2\sqrt3)}\\ &=8+2\sqrt{16-12}\\[6pt] &=12 \end{align} Therefore, $\sqrt{4+2\sqrt3}+\sqrt{4-2... | [
"76",
"1936",
"1304",
"1296"
] | B | Answer
Let √N/11= 4
Then √N = 11 x 4 = 44
∴ N = 44 x 44= 1936.
Correct Option: B |
AQUA-RAT | AQUA-RAT-38248 | \begin{align*} =&0.2016+0.1296+0.756+0.336+\\ & 0.864+0.504+0.224+0.324+ \\ &0.144+0.0084+0.0216+0.0036+\\ &0.0096+0.0056+0.002 \end{align*}
$=0.6976$
Edit: Thank you Vaibhav for providing an alternative method.
Alternate Method:
probability that the plane is hit when all the four shots are fired,
$P=1- \text{prob... | [
"0.6976",
"0.7013",
"0.789",
"0.8356"
] | A | Required probability:
=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)=(0.4×0.7×0.8×0.9)+(0.6×0.3×... |
AQUA-RAT | AQUA-RAT-38249 | Another way: If Alice is to win, it must be after an even number of tosses. So divide the sequence of tosses into pairs. Let D be the event two heads, and let M (mixed) be the event head then tail or tail then head. Each of D and M has probability $\frac{4}{9}$.
The ways Alice wins are D, MD, MMD, MMMD, and so on. So ... | [
"3/140",
"1/280",
"27/280",
"3/35"
] | C | P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*1/8*5/7 + 1/5*7/8*2/7 + 4/5*1/8*2/7 = 27/280.
Answer: C |
AQUA-RAT | AQUA-RAT-38250 | # Probability based on a percentage
We have a group of 15 people, 7 men and 8 women.
Randomly selecting 5 people, what's the probability to pick 3 men and 2 women? What's the probability to pick at least 1 man?
I tried solving the first question like this: $${7 \choose 3} = \frac{7!}{(7-3)!3!} = 35$$ and $${8 \choos... | [
"1/5",
"2/5",
"3/5",
"4/5"
] | C | Using the first example, here is the probability of THAT EXACT sequence occurring:
MMWW = (3/6)(2/5)(3/4)(2/3) = 36/360 = 1/10
Each of the other 5 options will yield the exact SAME probability....
eg
MWMW = (3/6)(3/5)(2/4)(2/3) = 36/360 = 1/10
So we have 6 different options that each produce a 1/10 chance of occurring.... |
AQUA-RAT | AQUA-RAT-38251 | reference-request, modelling, voting
For the election $(C, \{v\})$, i.e. with $v$ being the only vote, we have two admissible outcomes: $O_1 = \{p_\mathrm{rep} \mapsto 1, p_\mathrm{dem} \mapsto 0\}$ and $O_2 = \{p_\mathrm{rep} \mapsto 0, p_\mathrm{dem} \mapsto 1\}$. For $(C, \{v, v\})$, we have the same two outcomes. ... | [
"57%",
"60%",
"65%",
"90%"
] | A | Solution
Total number of votes polled= (1136 + 7636 + 11628) = 20400.
∴ Required percentage= ( 11628/20400x 100)%= 57%
Answer A |
AQUA-RAT | AQUA-RAT-38252 | $$(2)-(1')\Rightarrow f\, =\, -2e\, +\, 765 \: \: \: ---(3)\\ (3)\rightarrow (1)\Rightarrow 22e = 21(-2e+765)+319 \\ e=256 \\ f=253$$
The following is multiple choice question (with options) to answer.
(160)^2 - (161)^2 = | [
"1",
"100",
"229",
"323"
] | D | Using the formula:
(a+1)^2 - a^2 = 2a+1
So, Answer = 161*2 + 1
= 322+1 = 323 = Answer = D |
AQUA-RAT | AQUA-RAT-38253 | ### Show Tags
30 Oct 2018, 10:20
Bunuel wrote:
When a company places a wholesale order on coffee cups with the company logo, they pay $692 for 80 cups. When Phil wants to buy just one such cup, it costs him$12.50. How much above the wholesale price per cup is he paying?
A. $0.55 B.$3.85
C. $7.35 D.$10.65
E. $14.25 Th... | [
"1,108",
"3,300",
"2,108",
"2,124"
] | B | We have $200 and we have to maximize the number of hot dogs that we can buy with this amount.
Let's try to find out what is the maximum number of hot dogs that we can buy for a lesser amount of money, which in this case is 400 for $22.95.
For the sake of calculation, let's take $23. 23x8 gives 184 ,i.e. a total of 400x... |
AQUA-RAT | AQUA-RAT-38254 | in the comments section. At what speed does the second train B travel if the first train travels at 120 km/h. You can approach this as if you were solving for an unknown in math class or you can use the speed triangle. Time, Speed and Distance: Key Learnings. ) Since the distances are the same, I set the distance expre... | [
"85 km/h",
"82.66 km/h",
"87.67 km/h",
"90.25 km/h"
] | B | Ans.(B)
Sol. Total distance = 62 × 8 = 496 km
Now speed = 496/6 = 82.66 km/h |
AQUA-RAT | AQUA-RAT-38255 | # Reset the equation counter
\documentclass{article}
\usepackage{amsmath, amsfonts, chngcntr}
\newcounter{problem}
\newcounter{solution}
\newcommand\Problem{%
\stepcounter{problem}%
\textbf{\theproblem.}~%
\setcounter{solution}{0}%
}
\newcommand\TheSolution{%
\textbf{Solution:}\\%
}
\newcommand\ASolution{%
\stepcou... | [
"cnp",
"cn/p",
"(c + n)/p",
"cnp/(c + n)"
] | D | let t1 and t2 be the time taken to row upstream and downstream respectively
now,
t1=distance/speed=d/c
similarly,
t2=d/n (as same distance has to be rowed)
also,
t1+t2=p
therefore,
p=(d/c)+(d/n)
=d(c+n)/cn
d=pcn/(c+n)=D |
AQUA-RAT | AQUA-RAT-38256 | The (10/3t)/(7/3t) = 10/7 then the work ratios is 10 to 7
Since Time Ratio is the inverse of work, the the answer is 7 to 10
Bunuel wrote:
Machine X can complete a job in half the time it takes Machine Y to complete the same job, and Machine Z takes 50% longer than Machine X to complete the job. If all three machines... | [
"20 to 3",
"6 to 1",
"5 to 1",
"1 to 6"
] | A | The fastest worker who does 8 units of job worked for all 10 hours, so he did 8*10=80 units of job;
The slowest worker who does 2 unit of job worked for only 4+2=6 hours (first 4 hours and last 2 hours), so he did 2*6=12 units of job;
The ratio thus is 80 to 12, or 20 to 3.
Answer: A. |
AQUA-RAT | AQUA-RAT-38257 | Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink] 21 Apr 2017, 03:36
Go to page 1 2 Next [ 25 posts ]
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Topics:
16 A, B, C and D are positive integers such that A/B = C/D. Is C divisibl 7 16 Mar 2016, 06:12
5 For non–zero integers a, b, c and d, ... | [
"1 : 2",
"3 : 5",
"5 : 7",
"6 : 11"
] | A | Sol. A : B = 3 : 4, B : C = 4 : 5, C : D = 5 : 6
∴A∶B∶C∶D= 3 : 4 : 5 : 6.
Thus, A : D = 3 : 6 or, 1 : 2
A |
AQUA-RAT | AQUA-RAT-38258 | • One more thing. The only thing you must avoid in a proof of $y=z$ is starting with $y=z$ and deriving $0=0$ or $1=1$. As long as your proof starts with assumptions you are given, follows logically valid steps, and ends up with what you want, then the proof is good. Many of my students try to show $x=y$ and argue "$x=... | [
" y = -4 and z = -3",
" y = 4 or z = -3",
" y = -4 or z = 3",
" y = 1 and z = 3"
] | D | factor out:
(y-1)(z-3+5)=0
(y-1) (z+2) = 0
So by checking options we get ,
Ans - D |
AQUA-RAT | AQUA-RAT-38259 | A boy and his sister. When you subtract two from the boy’s real age and add two to his sister’s age, his sister
becomes twice his NEW (subtracted) age. If you subtract three from his real age instead and add three to his sister then she becomes thrice his NEW (subtracted) age. What are their real ages?
A little more de... | [
"32 years, 23 years",
"32 years, 29 years",
"35 years, 29 years",
"35 years, 33 years"
] | A | Explanation:
When Ravi's brother was born, let Ravi's father's age = x years and mother's age = y years.
Then, sister's age = (x - 28) years. So, x - 28 = 4 or x = 32.
Ravi's age = (y - 26) years. Age of Ravi's brother = (y - 26 + 3) years = (y - 23) years.
Now, when Ravi's brother was born, his age = 0 i.e. y - 23 = 0... |
AQUA-RAT | AQUA-RAT-38260 | Each of your methods gives you $1.496 \times 10^9 ~\rm{m}$ - accurate to 4 significant digits. That's better than you should expect.
The accuracy of your result is only ever as good as the accuracy of the inputs. Some of the data you have is given to 5 significant digits - that will give you the "more accurate" result... | [
"0.35%",
"0.34%",
"0.034%",
"0.035%"
] | C | Explanation:
Error = (81.5 - 81.472) = 0.028
Required percentage =
0.028/ 81.472×100=0.034
Option C |
AQUA-RAT | AQUA-RAT-38261 | # Reset the equation counter
\documentclass{article}
\usepackage{amsmath, amsfonts, chngcntr}
\newcounter{problem}
\newcounter{solution}
\newcommand\Problem{%
\stepcounter{problem}%
\textbf{\theproblem.}~%
\setcounter{solution}{0}%
}
\newcommand\TheSolution{%
\textbf{Solution:}\\%
}
\newcommand\ASolution{%
\stepcou... | [
"10 kmph",
"13 kmph",
"65 kmph",
"55 kmph"
] | A | Speed of the boat in still water
= (60+80)/2
= 70 kmph. Speed of the stream
= (80-60)/2
= 10 kmph.
Answer: A |
AQUA-RAT | AQUA-RAT-38262 | 1) Row 1: A-B, Row 2: C-D
2) Row 1: A-C, Row 2: B-D
3) Row 1: A-D, Row 2: B-C
4) Row 1: B-C, Row 2: A-D
5) Row 1: B-D, Row 2: A-C
6) Row 1: C-D, Row 2: A-B
Thus, for each group of 4 dogs chosen, there could be 6 teams. Therefore, the total number of teams that can be formed is 70 x 6 = 420.
_________________
# Jeffr... | [
"450",
"420",
"400",
"390"
] | D | Answer is D.
Total wolfs= 400 = 4 * Other Animals (X)
or X = 10.
So, Difference in wolfs and X = 400-10 = 390. |
AQUA-RAT | AQUA-RAT-38263 | python, python-3.x, datetime, reinventing-the-wheel
Furthermore, you can make is_leap_year a one-liner, since the if-else blocks and zero-comparisons are a bit verbose for my taste of "pythonicness":
def is_leap_year(year):
return not year % 4 and (year % 100 or not year % 400)
Also I find it a bit intricately, t... | [
"1200",
"800",
"700",
"2000"
] | C | Explanation :
1. Every year divisible by 4 is a leap year, if it is not a century.
2. Every 4th century is a leap year, but no other century is a leap year.
800,1200 and 2000 comes in the category of 4th century (such as 400,800,1200,1600,2000 etc).
Hence 800,1200 and 2000 are leap years
700 is not a 4th century, but i... |
AQUA-RAT | AQUA-RAT-38264 | = 4 52. Probability (statistics) What is the probability of getting a sum of 8 in rolling two dice? Update Cancel. Two fair dice are rolled and the sum of the points is noted. For example: 1 roll: 5/6 (83. of ways are - 1 , 1 1 , 2 2 , 1 1 , 4 4 , 1 1 , 6. The probability of rolling a specific number twice in a row is ... | [
"1/4",
"1/18",
"2/11",
"3/13"
] | B | n(S) = 6*6 = 36
E = {(5,6),(6,5)}
Probability = 2/36 = 1/18
Answer is B |
AQUA-RAT | AQUA-RAT-38265 | 27&305893372041&12,5,5,7,5,8\\ 28&801042337577&12,5,5,7,7,8\\ 29&2097687354880&12,5,7,7,7,8\\ 30&5493183075966&12,7,7,7,7,8\\ 31&14383060457018&12,7,7,7,7,10\\ 32&37658422859324&14,7,7,7,7,10\\ 33&98594676094434&14,7,7,9,7,10\\ 34&258133753770289&14,7,7,9,9,10\\ 35&675827901330148&14,7,9,9,9,10\\ 36&1769404155218244&14... | [
"12",
"9",
"1",
"3"
] | A | 12 is an even number. All other given numbers are odd
Answer : Option A |
AQUA-RAT | AQUA-RAT-38266 | 4. A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the pro... | [
"11",
"12",
"14",
"13"
] | D | D
13
Let the number of men initially be x. we have M1 D1 H1= M2 D2 H2
So, x * 65 * 6 = (3x)/4 * 40 * h2
=> h2 = (65 * 6 * 4)/(3 * 40) = 13. |
AQUA-RAT | AQUA-RAT-38267 | Examveda
# In an institute, 60% of the students are boys and the rest are girls. Further 15% of the boys and 7.5% of the girls are getting a fee waiver. If the number of those getting a fee waiver is 90, find the total number of students getting 50% concessions if it is given that 50% of those not getting a fee waiver... | [
"33%",
"34%",
"35%",
"36%"
] | A | assume total students =100 in that 35 students are boys ,remaining 65 are girls........
20% of boys(35) =7
40% of girls(65) =26
totally (26+7)=33 mens went to outing...... 33 is 33% in 100
so, the answer is 33%
ANSWER:A |
AQUA-RAT | AQUA-RAT-38268 | algorithms, scheduling, algorithm-design
Title: Schedule two trains whose tracks overlap so they don't crash I've encountered scheduling problems in my algorithms class before like the type we use vertex cover to solve.
Recently I was asked this question and did not even know what algorithmic technique to use to answe... | [
"7 4/5",
"9 3/5",
"4 1/6",
"7 7/12"
] | B | A + B + C's 1 day's work = 1/4
A's 1 day's work = 1/16
B's 1 day's work = 1/12
Therefore C's 1 day's work = 1/4 - ( A's 1 day's work + B's 1 day's work )
=> C's 1 day's work = 1/4 - ( 1/16 + 1/12 )
=> C's 1 day's work = (12-3-4)/48 = 5/48
So, C alone can do the work in 48/5 = 9 3/5 days.
So correct answer is B |
AQUA-RAT | AQUA-RAT-38269 | ## 1 Answer
Case 2:
3 < x < 6
|x-3|= (x-3)
|x-6|= -(x-6)
(x-3)-(x-6)<5
3<5
3<5 is true, so 3 < x < 6 is also solution for |x − 3| + |x − 6| < 5
Finally we have |x − 3| + |x − 6| < 5 $\Leftrightarrow$ 2 < x < 7
The following is multiple choice question (with options) to answer.
If |4x+6| = 46, what is the sum o... | [
"2",
"-2",
"4",
"-5"
] | B | There will be two cases
4x+6= 46 or 4x+6 = -46
=> x =10 or x= -12
sum of both the values will be -12 +10 = -2
Answer is B |
AQUA-RAT | AQUA-RAT-38270 | Difficulty:
65% (hard)
Question Stats:
53% (03:18) correct 47% (03:14) wrong based on 97 sessions
### HideShow timer Statistics
Question of the Week #7
Three pipes P, Q, and R are attached to a tank. P and Q individually can fill the tank in 3 hours and 4 hours respectively, while R can empty the tank in 5 hours.... | [
"17 1/4 min",
"28 1/7 min",
"15 min",
"17 1/8 min"
] | C | 1/20 + 1/30 - 1/60 = 4/60 = 1/15
15/1 = 15
Answer:C |
AQUA-RAT | AQUA-RAT-38271 | We're asked for the price at which the TOTAL PROFIT from the sale of these units = $42,000. Since there are 600 units, then each unit has to bring in$42,000/600 = $70 in profit. The COST of each unit is$90, so to hit that total profit, we just need to increase that $90 by$70 on each unit.
$90 +$70 = $160 Final Answer:... | [
"130",
"100",
"70",
"150"
] | B | Explanation :
Cost price function f(x) = cx2 + bx + 240.
When x = 20, f(20) = 400c + 20b + 240.
=> f(40) = 1600c + 40b + 240
66.67% is 2/3.
=> f(40) – f(20) = 2/3 * f(20).
Substituting f(40) and f(20), we get, 1200c+ 20b =(2/3) * (400c + 20b + 240)
Solving, we get 20b + 2800c = 480.
Now, f(60) = 3600c + 60b + 240.
f(60... |
AQUA-RAT | AQUA-RAT-38272 | homework-and-exercises, work, potential-energy
Title: Problem regarding finding work done This problem is given in my physics book. How much work will be done if anyone wants to stack up 12 bricks? Given that each brick is $10 cm$ high and each brick's mass is $2 kg$. ($g=9.8$)
Now in finding my answer I used the mass... | [
"320",
"340",
"300",
"310"
] | B | Area of the floor = 4m x 5m = 20 m2
17 bricks are needed to make 1 m2 area.
So to make 20 m2 no of bricks needed = 17 x 20 = 340 Answer : B |
AQUA-RAT | AQUA-RAT-38273 | -
You say the answer is 1/2 and seem to argue that the answer is 2/3. – Aryabhata Aug 18 '10 at 20:10
He says the answer is 2/3 for the cards example, which is correct, not for the boys/girls paradox, which should be 1/2 and he so states in the opening paragraph. – Abel Aug 18 '10 at 20:24
Ok, I clarified. – Nate El... | [
"1/3",
"2/5",
"2/7",
"3/8"
] | B | Probability that only one of them is selected = (prob. that brother is selected) × (prob. that sister is not selected) + (Prob. that brother is not selected) × (Prob. that sister is selected)
= = 2/5
B |
AQUA-RAT | AQUA-RAT-38274 | # Making Friends around a Circular Table
I have $n$ people seated around a circular table, initially in arbitrary order. At each step, I choose two people and switch their seats. What is the minimum number of steps required such that every person has sat either to the right or to the left of everyone else?
To be spec... | [
"3!",
"8!",
"7!",
"9!"
] | D | Ans.(D)
Sol. Total number of persons = 10 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 9 places in 9P9 = 9! Ways ... The number of required arrangements = 9! x 1= 9! = 9! ways |
AQUA-RAT | AQUA-RAT-38275 | So the 1st question you needed to answer was how much distance do they cover together per hour (we just did that), now the next question to answer is how long it takes to cover 810km in total distance at their effective speed.
• it means that if they are covering 135km each our then they would be meet together in 135x... | [
"a) 66.67-x",
"b) 40-x",
"c) 80-2x",
"d) 120-x"
] | A | Let's say the two cars have speeds V1 and V2. The fact that they are moving in opposite direction means that their relative speed is (V1 + V2). In other words, any gap between them will be changing in size at a rate of (V1 + V2). It doesn't matter whether they are moving toward each other or away from each other. If th... |
AQUA-RAT | AQUA-RAT-38276 | \prod_{i=1}^m \frac{ \omega^{r_i s_j} + \omega^{-r_i s_j} }2 \right\rangle_{r,s} \ . \hspace{1cm} (4)$$ Note that we have also changed the order of the product operations over $i$ and $j$ here. Now the average over the $s_j$ can be performed easily: for each $j$, $$\left\langle \prod_{i=1}^m \frac{ \omega^{r_i s_j} + \... | [
"2989",
"2765",
"5800",
"2989"
] | C | Total production of salt by the company in that year
= 5000 + 5150 + 5300 + .... + 6650 = 70050.
Average monthly production of salt for that year
= 70050/12
= 5837.
Answer:C |
AQUA-RAT | AQUA-RAT-38277 | kinematics, speed, distance
Title: How to calculate the speeds two objects need to move at in order to reach different destinations at the same time For example: On a graph there are two points. Each point has a different destination. The distance between Point A and its destination is 50, and the distance between Poi... | [
"30 km",
"40 km",
"50 km",
"60 km"
] | D | in 2 hours a covers (10+20)=30 km
b covers( 5+10)=15 km, total covered=45
in the next hour they have to cover (90-45) km with the speeds 40km/hr and 20 km/hr respectively
let them take another t hrs to meet
so sum of the distance to be covered by both is 45km
(40*t)+(20*t)=45km
gives t= (3/4) hrs
we need to fid out the... |
AQUA-RAT | AQUA-RAT-38278 | • You for $v_x=0$. What does that imply about $u_x,u_y,v_y$? – N. S. Jul 9 '14 at 12:58
• Ouch. So $u=c_1,v=c_2\quad (c_{1,2}\in\mathbb{C})$ ? but that's a constant function (not sure whether they asked for a linear function with incline $\neq 0$). Thanks. – user65985 Jul 9 '14 at 13:05
The following is multiple choic... | [
"II",
"I and II",
"I and III",
"II and III"
] | B | u@v = u^2 - uv=u(u-v).... so u@v will be zero if u=v or u=0.. but u cannot be equal to 0.. as per Q, x and y can take any int value except 0...
now lets look at the choices..
when x=y, it will be 0... so ok...
when we put xy=y, it is possible when x=1 and y any integer... so ok again
when we put x=x+y.... only possibil... |
AQUA-RAT | AQUA-RAT-38279 | Given: Pat bought 5 pounds of apples.
Target question: How many pounds of pears could Pat have bought for the same amount of money?
This is a good candidate for rephrasing the target question.
Let A = the price per pound of apples
Let P = the price per pound of pears
If Pat bought 5 pounds of apples, then 5A = the to... | [
"100% less than N",
"200% less than N",
"Equal to N",
"100% greater than N"
] | D | Correct answer is (D).
This year, the price of a tree is price1=P/N.
If this price decreases by 50% it becomes Price2=P/N*0.5
Then with P dollars, you can grow P/Price2 trees i.e. P/(P/N*0.5) i.e. N/0.5 i.e. 2*N
Which is 100% greater than N. |
AQUA-RAT | AQUA-RAT-38280 | The sum $$S$$ can be written in terms of the first number in the interval, $$a$$, and the length of the interval $$k$$. We have $$S = k(a + (k-1)/2)$$, or $$k$$ times the median of the sequence. For many $$a$$, one can pick a number c next to and different from the median, and c will be coprime to the integer which is ... | [
"0",
"1",
"2",
"3"
] | A | Mean = (1 + 2 +3 + 4 + 5 + 6 + 7)/7 = 4
Median = 4
Difference = 4-4 = 0
Option A |
AQUA-RAT | AQUA-RAT-38281 | are these 2's supposed to be squares?
RonL
7. Originally Posted by CaptainBlack
this last line should be:
=> x = (k/3) pi for k an integer
RonL
right, i forgot about the 1/3
The following is multiple choice question (with options) to answer.
If x/y is an integer, which of the following must also be not an integer?
... | [
"I alone",
"II alone",
"III alone",
"I, II and III"
] | D | Let's take X = 4/3 and Y = 2/3
Then X/Y = 2 which is an integer.
But XY = 4/3 * 2/3 = 8/9 --> Not an integer.
Y/X = 2/3 divided by 4/3 = 2/4 = 1/2 Not an integer.
X alone is 4/3. Not an integer.
Hence D. |
AQUA-RAT | AQUA-RAT-38282 | permutations around a round table with labelled seats
Two men, Adam and Charles, and two women, Beth and Diana, sit at a table where there are seven places for them to sit down. Two people are sitting next to each other if they occupy consecutive chairs. A non-trivial rotation defines a different seating arrangement, ... | [
"24",
"48",
"72",
"74"
] | C | When the constraint on an arrangement says,Two people should not be seated together,we do just the opposite. We make them sit together! Kind of tie them with a thread and assume they are one unit!
Let's see why....
These 5 people can be arranged in 5! ways. These are the total number of ways you get.
Now, when we tie 2... |
AQUA-RAT | AQUA-RAT-38283 | Manager
Joined: 07 Jul 2016
Posts: 79
GPA: 4
Re: Two bottles are partially filled with water. The larger bottle current [#permalink]
### Show Tags
04 Aug 2016, 22:33
AbdurRakib wrote:
Two bottles are partially filled with water. The larger bottle currently holds $$\frac{1}{3}$$ of its capacity. The smaller bottle, w... | [
" $0.25",
" $0.01",
" $0.05",
" $0.03"
] | B | Cost per capsule in R is 8.25/250=0.825/25=0.033
Cost per capsule in T is 2.99/130=0.023
The difference is 0.01
The answer is B |
AQUA-RAT | AQUA-RAT-38284 | # Chapter 7: Coordinate Geometry
1. If the point A (x , y) is equidistant from B (4 , 2) and C (-2 , 4). Find the relation between x and y.
|AB| = $$\sqrt{(x-5)^{2}+(y-1)^{2}}$$
= $$\sqrt{x^{2}+16-8x+y^{2}+4-4y}$$
|AC| = $$\sqrt{(x+2)^{2}+(y-5)^{2}}$$
= $$\sqrt{x^{2}+4+4x+y^{2}+16-8y}$$
Since, |AB| = |AC|
$$\Rig... | [
"17",
"16.3",
"18",
"19"
] | A | Use the formula of the distance formula
square root (x2-x1)^2+(y2-y1)^2
Do this for each of the sides and then the value is given as A. |
AQUA-RAT | AQUA-RAT-38285 | # Clarification on language of a question on profit and loss.
The question is:
By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage.
1. 33 1/3%
2. 33 1/2%
3. 33%
4. 34 1/4%
The answer provided by the book says it's the first one.
But if he gains the cost of 11 meters sh... | [
"337.33",
"280.33",
"299.33",
"268.33"
] | D | x*(85/100) = (460 - x)119/100
x = 280
Answer: D |
AQUA-RAT | AQUA-RAT-38286 | kmph. com/2016/01/01/speed-distance-timeVideos, worksheets, 5-a-day and much more. If a car traveled 50 miles over the course of one hour then its average speed will be 50 mph. Distance, Time and Speed Word Problems | GMAT GRE Maths. Exercise: Problems on Speed Time and Distance. org/time-speed-distanceTime, Speed and ... | [
"9.6",
"10.6",
"4.3",
"2.5"
] | B | Since we're not given a distance to work with, we can TEST any distance that we like. Here, since the speeds are 16km/hour and 8 km/hour, using a multiple of both 16 and 8 would make the math easiest.
Let's set the Distance up the hill at 64 km.
So, going uphill, we have....
D = (R)(T)
64 = (16)(T)
64/16 = 4 = T
4 hour... |
AQUA-RAT | AQUA-RAT-38287 | c) $$\frac{1}{15,000}$$ percent
d) $$\frac{1}{4,000}$$ percent
e) $$\frac{1}{40}$$ percent
Let x = the desired percent
In other words: 2.5 million is x percent of 10 billion
In other words: 2,500,000 = x% of 10,000,000,000
In other words: 2,500,000 = (x/100)(10,000,000,000)
Divide both sides by 100,000 to get: 25 =... | [
"657",
"765",
"865",
"840"
] | D | 25% of x = x/4 ; 15% of 1500
= 15/100 * 1500 = 225
Given that, x/4 = 225 - 15
=> x/4 = 210 => x = 840.
Answer:D |
AQUA-RAT | AQUA-RAT-38288 | (1\times3\times7\times9)^{\left\lfloor\frac{n}{10}\right\rfloor}\times\epsilon\equiv 9^{\left\lfloor\frac{n}{10}\right\rfloor}\times\epsilon$, where $\epsilon$ is either $1$, $3$ or $9$ depending on $n$ the last digit of $n$. These two reduction rules together with the modular reduction of $n\underset{5}{!}$ cut the si... | [
"814",
"802",
"836",
"900"
] | A | L = 15 M 17 CM =1517 CM
B = 9 M 2 CM = 902 CM^2
AREA = 1517 * 902 CM^2
FIND OUT HCF = 41
AREA OF SQUARE = 41 * 41 = 1517 * 902 / 41 * 41 = 37 * 22
=407 * 2 =814
ANSWER A |
AQUA-RAT | AQUA-RAT-38289 | Let one woman complete the job in $$w$$ days and one man in $$m$$ days.
First equation:
It takes 6 days for 3 women and 2 men working together to complete a work:
As the rate of 1 woman is $$\frac{1}{w}$$ job/day, then the rate of 3 women will be $$\frac{3}{w}$$ job/day. As the rate of 1 man is $$\frac{1}{m}$$ job/day... | [
"12/9 days",
"30/11 days",
"82/8 days",
"22/76 days"
] | B | 2M = 6W ---- 20 days
12M + 8W -----?
36W + 8 W = 44W ---?
6W ---- 20 44 -----?
6 * 20 = 44 * x => x = 30/11 days
Answer:B |
AQUA-RAT | AQUA-RAT-38290 | 4. A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the pro... | [
"Q=60",
"Q=70",
"Q=75",
"80"
] | C | We can also use the concept of man-days here
100 days -->10men so the job includes 100*10=1000 man-days
After 20 days
1/4 of Job is completed so 1/4 X 1000 man-days=250 man-days Job is done
Now the Balance Job=1000-250=750 man-days worth of Job
Since 2 men are fired so B/L men=8
Therefore Total no. of days of Job=750 m... |
AQUA-RAT | AQUA-RAT-38291 | WAIT!
S=11!
Because we have 11! ways of arranging the 11 items.
Sorry about that.
5. Hello, sweeetcaroline!
Edit: Plato is absolutely right . . . *blush*
6 red beads, 4 white beads, and 1 blue bead are placed in a line in random order.
What is the probability that no two neighboring beads are the same color?
There... | [
"64",
"65",
"66",
"67"
] | B | The repeated pattern R-R-R-G-G-G-G-Y-Y-Y-B has 11 beads.
But the missing section includes R-R-R-G-G-G-G-Y-Y-Y at the end.
Thus the number of beads in the missing section has the form 11k + 10.
The answer is B. |
AQUA-RAT | AQUA-RAT-38292 | 4. A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the pro... | [
"227.04 mtrs",
"378.4 mtrs",
"478.4 mtrs",
"488.4 mtrs"
] | A | If 20 men can build a wall 66 metres long in 10 days,
length of a similar wall that can be built by 86 men in 8 days = (66*86*8)/(10*20) = 227.04 mtrs
ANSWER:A |
AQUA-RAT | AQUA-RAT-38293 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$v = u – at$$ $$=> 30 = 60 – 1xt$$ $$=> t = 30s$$ At 30s, distance covered is: $$S = ut – ½ at^2$$ $$= 60 x 30 – ½ x 1 x (30)2$$ $$= 1800 – (15 x 30)$$ $$= 1800 – 450$$ $$= 1350m$$ (from the initial 90... | [
"50",
"88",
"65",
"55"
] | C | Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 49 - 36 = 13 km/hr.
= 13 * 5/18 = 65/18 m/sec.
2x/36 = 65/18 => x = 65.
Answer:C |
AQUA-RAT | AQUA-RAT-38294 | ## A number of people shared a meal, intending to divide the cost evenly among themselves. However, several of the diners
##### This topic has expert replies
Legendary Member
Posts: 2898
Joined: 07 Sep 2017
Thanked: 6 times
Followed by:5 members
### A number of people shared a meal, intending to divide the cost evenl... | [
"a) 5$",
"b) 3 $",
"c) 7 $",
"d) 4 $"
] | C | we got total 8 sandwiches ....we are dividing equally in 3 people.
per person: 8/3
initially
p:8
W:3
r:0
now since r ate 8/3 so he is paying 8 dollars for 8/3 sandwiches.
now p also ate 8/3 of his 5 sandwiches = so he gave 5-8/3 to r ==>7/3 to r
ok we have 8 dollars for 8/3 sandwich
therefore for 7/3 sandwich we will g... |
AQUA-RAT | AQUA-RAT-38295 | 5. Hello, James!
Another approach . . .
12 Students are in a class.
Five can go to room A, Four to room B, and Three to room C.
How many ways can this happen?
Assign 5 students to room A.
. . There are: . $_{12}C_5 \:=\:\frac{12!}{5!7!} \:=\:792$ ways.
From the remaining 7 students, assign 4 students to room B.
. .... | [
"1200 lt",
"1555 lt",
"1674 lt",
"1728 lt"
] | C | Given that
4 cars running 10 hrs a day consume 1200 lts. of fuel in 10 days.
1 car consumption per hour per day = 1200 /4 *10 *10 = 3 litre
Now question say new car consume 20% less fuel than the company’s four cars = 75/100 of 3 = 2.25 ( 25 percent less than 3)
Hence we calculate total consumption for next 6 days, the... |
AQUA-RAT | AQUA-RAT-38296 | ### Show Tags
09 Oct 2015, 14:30
jimjohn wrote:
If x, y, and z are integers greater than 1, and (3^27)(35^10)(z) = (5^8)(7^10)(9^14)(x^y), then what is the value of x?
(1) z is prime
(2) x is prime
I found an almost identical question with the same question stem, but different statements.
Here it is: if-x-y-and-z-a... | [
"0",
"2",
"4",
"6"
] | A | The number 52,428,800,000 is not divisible by 3. (We can verify this by adding the digits of the number to see that the sum is not a multiple of 3.)
Thus x = 0 and xy/z = 0.
The answer is A. |
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